Question

What is the present value of $3,325 per year, at a discount rate of 8 percent, if the first payment is received 7 years from now and the last payment is received 22 years from today?

Answer 1

Step-by-step explanation:

To calculate the present value of an annuity, we need to use the present value formula:

PV = C x ((1 - (1 + r)^-n) / r)

Where:

PV = present value

C = annual cash flow

r = discount rate

n = number of years

In this case, C = $3,325, r = 8%, and n = 22 - 7 = 15 (since the first payment is received 7 years from now and the last payment is received 22 years from today).

Using these values, we can calculate the present value of the annuity:

PV = $3,325 x ((1 - (1 + 0.08)^-15) / 0.08)

PV = $3,325 x ((1 - 0.2367) / 0.08)

PV = $3,325 x (0.7633 / 0.08)

PV = $3,325 x 9.5412

PV = $31,737.27

Therefore, the present value of the annuity is $31,737.27.